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R. Feng and H.Wu recently established a certain mean-value formula for the coordinates of the n-division points on an elliptic curve given inWeierstrass form (A mean value formula for elliptic curves, 2010, available at http://eprint.iacr.org/2009/586.pdf). We prove a similar result for the x and y-coordinates on a twisted Edwards elliptic curve.
Moody, D.
(2011),
Mean Value Formulas for Twisted Edwards Curves, Journal of Combinatorics and Number Theory, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=907010
(Accessed December 3, 2023)